Rewrite as a simplified fraction. ${0.\overline{19} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 19.1919...\\ 1x &= 0.1919...\end{align*}}$ Subtracting the two equations, we have: ${99x = 19}$ ${x = \dfrac{19}{99}} $